Isotopes are extensively used in forensic science for various applications, including the identification of unknown materials and the tracing of geographical origins. Isotopic analysis can determine the isotopic signature of materials, which can be unique to specific geographic locations or manufacturing processes. For example, the isotopic composition of elements like carbon, nitrogen, and oxygen in human hair can reveal information about a person's diet and geographical movements. This is because the isotopic ratios in food and water consumed are influenced by regional factors and are reflected in the body's tissues. Similarly, isotopes can be used to trace the origin of drugs, explosives, and other materials by matching their isotopic signatures with known samples. This technique provides a powerful tool in forensic investigations, offering clues that can link suspects to crime scenes or trace the origins of illicit materials.

Isotopes of the same element can form different molecules, referred to as isotopologues. These molecules have the same chemical structure and bonding but differ in the isotopic composition of one or more atoms. For example, water (H₂O) can exist as H₂¹⁸O, where one or both of the hydrogen atoms are replaced with the heavier isotope oxygen-18 (¹⁸O) instead of the more common oxygen-16 (¹⁶O). While isotopologues have nearly identical chemical properties, they can exhibit slight differences in physical properties like boiling and melting points. These variations are primarily due to the differences in mass, which can affect the vibrational frequencies of the molecules. Isotopologues are particularly useful in scientific research, especially in spectroscopy and environmental science, where they are used to trace chemical pathways and understand reaction mechanisms.

The atomic weight of an element on the periodic table is a weighted average of the atomic masses of all its naturally occurring isotopes. This value takes into account not only the mass of each isotope but also their relative abundances in nature. For instance, an element with two isotopes, where one is significantly more abundant than the other, will have its atomic weight more closely reflecting the mass of the more abundant isotope. This weighted average is important because it represents the mass of an element as it is typically found in nature, rather than a singular, fixed mass number. When calculating the atomic weight, chemists use the formula: atomic weight = Σ(isotope mass × isotope abundance), where the sum is over all isotopes of the element. This accounts for the fact that a sample of a natural element always contains a mixture of isotopes.

In palaeoclimatology, the study of historical climates, isotopes play a crucial role in reconstructing past environmental conditions. Isotopic analysis, particularly of oxygen and hydrogen isotopes, is used to deduce temperature variations, precipitation patterns, and oceanographic changes. For instance, oxygen isotopes (¹⁶O and ¹⁸O) in ice cores and marine sediments can indicate historical temperature fluctuations. The ratio of these isotopes changes with temperature; during colder periods, more ¹⁶O is trapped in ice sheets, while ¹⁸O is more prevalent in ocean water. By measuring the ratio of these isotopes in ice cores and sediment layers, scientists can infer historical temperature changes. Similarly, the ratio of deuterium (hydrogen-2 or ²H) to hydrogen in water samples provides insights into past precipitation patterns. This isotopic analysis offers a window into understanding Earth's climate history, aiding in the prediction of future climate trends.

Some isotopes are unstable and emit radiation as they decay into more stable forms. This radioactive decay occurs because the nucleus of the isotope has an imbalance in the number of protons and neutrons, leading to instability. There are different types of radioactive decay, including alpha, beta, and gamma decay, each involving the emission of different particles or energy. In medical applications, radioactive isotopes are used both in diagnostic imaging and in treatment. For instance, in diagnostic imaging, isotopes such as Technetium-99m (⁹⁹mTc) are used in radiopharmaceuticals. These isotopes emit gamma rays that can be detected by imaging equipment, allowing doctors to visualize internal structures and functions of the body. In treatment, isotopes like Iodine-131 (¹³¹I) are used in radiotherapy, particularly for thyroid cancer. The isotope concentrates in the thyroid gland and emits beta particles, destroying cancer cells while minimizing damage to surrounding healthy tissues. The controlled use of radioactive isotopes in medicine leverages their unique properties to diagnose and treat various medical conditions effectively.